Scaling theory of driven polymer translocation

TL;DR

This paper develops a scaling law for driven polymer translocation time considering pore-polymer interactions, and demonstrates how to rescale data to reveal asymptotic behavior, also extending the theory to include hydrodynamic interactions.

Contribution

It introduces a rescaling method to account for pore-polymer interactions in the translocation time scaling law and extends the theory to hydrodynamic interactions.

Findings

Rescaled translocation time exponent reaches asymptotic limit.

Pore-polymer interactions cause finite size effects.

Hydrodynamic interactions do not alter the fundamental scaling relation.

Abstract

We present a theoretical argument to derive a scaling law between the mean translocation time $\tau$ and the chain length $N$ for driven polymer translocation. This scaling law explicitly takes into account the pore-polymer interactions, which appear as a correction term to asymptotic scaling and are responsible for the dominant finite size effects in the process. By eliminating the correction-to-scaling term we introduce a rescaled translocation time and show, by employing both the Brownian Dynamics Tension Propagation theory [Ikonen {\it et al.}, Phys. Rev. E {\bf 85}, 051803 (2012)] and molecular dynamics simulations that the rescaled exponent reaches the asymptotic limit in a range of chain lengths that is easily accessible to simulations and experiments. The rescaling procedure can also be used to quantitatively estimate the magnitude of the pore-polymer interaction from simulations or experimental data. Finally, we also consider the case of driven translocation with hydrodynamic interactions (HIs). We show that by augmenting the BDTP theory with HIs one reaches a good agreement between the theory and previous simulation results found in the literature. Our results suggest that the scaling relation between $\tau$ and $N$ is retained even in this case.